Masterminding a project to model a coral reef in crochet, Margaret Wertheim hopes to share some of the most complicated mathematical models embodied in our universe with the minds (and hands) of the masses. TED’s film + video editor Kari Mulholland talked with Margaret Wertheim last week about the Crochet Coral Reef — as well as her theories of kindergarten, the beauty of pi, and the next homes for the Reef. For the full interview, hit the jump. A sample:

There is no such thing as a perfect hyperbolic surface in nature. After crocheting mathematically curved surfaces for about two years, Chrissy came in one day and said, you know what? I’m really sick of crocheting perfectly, I’m sick of all the geometry. I want to try something irregular. So what would happen, for instance, if I crocheted at variable rates? What would happen if I increase a bit faster on this side of the model and a bit slower on that side?

As soon as we started to mix these variations, the whole thing immediately looked more natural. And we realized this is what nature’s doing. Nature doesn’t feel compelled to stick to a mathematically precise algorithm; in fact, nature probably can’t stick to an algorithm. Conditions in the water, amount of sunlight, availability of nutrients would all cause an organism to grow a bit faster in one direction then in the other. That’s what we realized we were doing with these varying rates of increase; we were simulating various conditions that might happen in nature.

That is in fact a true statement. There are some really big problems that you have to overcome in order to be able to model hyperbolic space on a computer.

One is that hyperbolic space is not a structure that can be described analytically. Most computer modeling programs, where we see smooth surfaces, are based on having an analytic understanding of the structure and then setting out to make a digital representation of it.

Another challenge is the same one faced by the animation industry; it’s the problem of what to do with fabric. To work with a flat piece of fabric is easy, but once fabric has to sit in a three-dimensional space and swoosh around in relationship to what is supposed to be a simulated physical world, that is a really huge challenge.

The same challenge arises when simulating the texture of the skin or the way skin moves when faces are animated in computer programs. They actually model underlying bone structure and the skin is then treated like a fabric that is draped across the substructure of the bone.

These are problems in geometry. One of the great sources of employment for people with PhDs in geometry is the animation industry.

It’s a very interesting thing that we think, “If I can do it with my hands, I must be able to do it on the computer much more easily.” Why do we jump to that conclusion?

Computers are very powerful tools, but in the simulated world of the computer, everything has to be calculated. We are moving into the age of being able to simulate more and more things on computers and we are coming to realize how mind-bogglingly complex the world is which we are trying to simulate. The fall of a handkerchief in the wind is hard to simulate, and yet the handkerchief does it effortlessly. In some sense, the handkerchief knows something; it can do something that our best computer engineers can’t do. The sea slugs with their hyperbolic frills are smarter than the geometers with their faces in the computers.

It does raise a philosophical question about how does the world, how do simple things like handkerchiefs, sea slugs, and corals do these things without computers? What I am trying to say is that the symbolic representation that has to be used when we use computers is not the only form of knowledge, there are other representations of knowledge that are just as powerful and probably even more powerful; and that is the physical manifestation of knowledge.

When did you become aware of these physical manifestations of figures?

I think that my love of figures and figuring is a thing that’s bound up with my childhood. When I was in grade three or four, my mathematics teacher, a man named Mr. Marshall, gave us a mathematics lesson about circles. The whole point of this lesson was to teach us about pi; the magical number that is at the heart of all circles.

Instead of simply telling us the formula for the circumference of a circle and the area of a circle, he gave us an entire lesson letting us discover pi for ourselves. For me, the exercise worked. I looked around me and I realized that every time I see a dinner plate, every time I see the sun or the moon, every time I see the wheel of a car, every time I see a circle in the world around me, that this magical number pi is embedded in it.

I will never forget this moment; it was truly like a revelation to me, that this almost angelic thing pi was hovering magically, like an angel behind the material world. I had several experiences like that during my childhood.

I think that these teachers who allow us to discover these figures for ourselves without just telling us “Here’s the knowledge” actually enable what all great mathematicians experience when they make discoveries. You are coming face to face with a new species or entity that you’ve never seen before.

These very simple active engagements have the power to embed ideas in your mind. If I could do anything in my life and be remembered for anything, I would like to be remembered for helping the world see the value of physical engagement with ideas. And I, by no means, make the claim to be the first person to have thought of this. All sorts of people have done this through the ages, like Friedrich Fröbel.

You mention Friedrich Fröbel at the end of your talk. Could you explain a bit more about his teaching methodology?

Friedrich Fröbel (or Friedrich Froebel) ought to be a name that everyone on planet Earth knows. We all do know the system that he created — kindergarten — although we all experience kindergarten in a very debased, watered-down form, to the one that Fröbel created in the mid-19th century. He ought to be an absolute hero of the entire world, for the educational system that he created for little children.

The form of engagement that Fröbel introduced is what I’m trying to do with the Institute for Figuring. I was lucky enough, but of course I didn’t know it at the time, to have teachers who allowed me full engagement with ideas and I think that it’s a tragedy of our society that we lost this methodology of learning.

For those of us who would like to learn how to play with ideas and would like to teach our children these methods, what would you suggest?

Read a book called Inventing Kindergarten by a man named Norman Brosterman. He is a dear friend of mine. Inventing Kindergarten is a book about the history of kindergarten and is an absolute delight to read. I also suggest reading Fröbel’s On the Education of Man, which is about the kindergarten system as it existed in its heyday in the late nineteenth century. It will absolutely blow your mind.

I would like to see a Fröbelian renaissance. For individuals who would like to integrate these teachings in their own lives rather than wait for Fröbelian schools to somehow manifest, our site has a number of resources for things that you can do and we have a number of online exhibits from which you can download models.

Could you explain how a regular crochet stitch becomes hyperbolic?

Basically what you do is crochet three stitches and then increase one stitch in the next stitch. You can increase every third stitch, every fifth stitch, or every tenth stitch, as long as you keep it regular, as long as you always increase at the same rate. When you do this, all of the models have a tendency to look pretty much the same. They can be different colors, they can be different sizes, but they tend to have similar looks because there is actually one mathematical structure.

There is no such thing as a perfect hyperbolic surface in nature. After crocheting mathematically curved surfaces for about two years, Chrissy came in one day and said, you know what? I’m really sick of crocheting perfectly, I’m sick of all the geometry. I want to try something irregular. So what would happen, for instance, if I crocheted at variable rates? What would happen if I increase a bit faster on this side of the model and a bit slower on that side?

As soon as we started to mix these variations, the whole thing immediately looked more natural. And we realized this is what nature’s doing. Nature doesn’t feel compelled to stick to a mathematically precise algorithm; in fact, nature probably can’t stick to an algorithm. Conditions in the water, amount of sunlight, availability of nutrients would all cause an organism to grow a bit faster in one direction then in the other. That’s what we realized we were doing with these varying rates of increase; we were simulating various conditions that might happen in nature.

Do you think communities have become more aware of nature and the plight of coral reefs through their participation in the Crochet Reef Project?

There are two environmental aspects to this project: one is that we are trying to bring some awareness to the plight of coral reefs due to global warming but the other environmental aspect that is really critical for the oceans is that our oceans are being devastated by the tsunami of plastic trash. Captain Charles Moore gave a beautiful presentation at TED about that. And it is really one of the most important environmental issues on our planet at the moment. A huge island of plastic garbage is building up in the Pacific Ocean. It is twice the size of Texas, thirty meters deep, and growing everyday.

When Chrissy and I heard about this floating plastic garbage island, we started crocheting the satanic sibling of the Crochet Reef — The Toxic Reef. The Toxic Reef is made out of plastic trash, specifically our plastic trash. We made a commitment when we started this reef that we would start keeping our own plastic trash to see how much we used.

We have actually been doing this now for over two years. When we started doing this we thought we were pretty ecologically sound, but by the end of the first week we were appalled, and by the end of the first month we couldn’t believe it. We started to change our practices. I had to make lifestyle changes. I tried to eat less take out dinners, I shopped from markets where I could buy fresh fruits and vegetables and could avoid buying things in plastic containers. It is really, really hard.

Scientists who have studied our plastic consumption have said it is completely unrealistic to expect the world to shut off the plastic spigot tomorrow. But we can cut down. This is a problem that has arisen literally in my lifetime. If it has arisen, it can subside.

When we have workshops, we encourage our contributors to collect their own trash for at least a week. Become aware of how much plastic trash that you personally use and you will be shocked. Awareness is the first step.

Do you have any updates on the Crochet Reef Project since TED?

Just in the two months since TED some really fantastic things have happened. We’ve been invited to show the project at the Smithsonian National Museum of Natural History in Washington, DC. It will be shown in the Hall of Ocean Science. It’s a really great honor because it is the first time ever that the Smithsonian National Museum of Natural History will show an art project.

The reason they are doing this is because the project has a huge amount of science content and the other reason is because they really value the fact that this project has a huge community outreach component. The big trend among many of the major art institutions now is towards community involvement. We are also going to show the Bleached Reef at another part of the museum called Cooper-Hewitt, which is the National Design Museum in New York City.

I just wanted to add finally that people often ask me what the Crochet Reef Project is about. Is it art, is it science, is it math is, it handicraft, is it environmental consciousness raising? Which of these is it? And in a very real sense it is all of the above.

It is also something else: it is feminism. It is feminism at work in one of the very best dimensions. It is saying women’s unique talents and skills are valuable and have a place in the world. We have the work of housewives showing in some of the most important museums in our culture. Every single one of the people who have participated in this project, and many of them are middle age women, tell us again and again how important it is for them to see their work valorized and taken seriously in this way. It is powerful to see their domestic craft presented as an equal to the realm of higher mathematics; these two things are not as far apart from one another as we are often led to believe.